Subgroups — C₂×#41×D₅₂ #16769882

Order 3328.

12314 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₁₃	C₂	1	2	yes	maximal, complemented
2	#41×D₅₂	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719282	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719281	C₂	1	2	yes	maximal, complemented
6	C₂×#11719260	C₂	1	3	yes	maximal, complemented
7	C₂×#11719259	C₂	1	6	yes	maximal, complemented
8	C₂×D₄×D₅₂	C₂	1	3	yes	maximal, complemented
9	C₂×#11719182	C₂	1	3	yes	maximal, complemented
10	C₂×#11719229	C₂	1	6	yes	maximal, complemented
11	C₂²×C₄×D₅₂	C₂	1	3	yes	maximal, complemented
12	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×#41×D₁₃	—	2	32	no	—
15	C₂×#41×D₁₃	C₂²	1	32	yes	complemented
16	C₂²×#6131	C₂²	1	2	yes	complemented
17	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
18	C₂²×#6129	C₂²	1	6	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	6	yes	complemented
20	C₂²×#6127	C₂²	1	6	yes	complemented
21	C₂³×D₅₂	C₂²	1	3	yes	—
22	C₂³×C₄×D₁₃	C₂²	1	6	yes	complemented
23	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
27	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
28	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
29	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
30	C₂×#88184	C₂²	1	6	yes	complemented
31	C₂×#88184	C₂²	1	6	yes	complemented
32	C₂²×#6103	C₂²	1	6	yes	complemented
33	C₂²×C₄⋊Dic₁₃	C₂²	1	3	yes	complemented
34	#11719282	C₂²	1	16	yes	complemented
35	#11719281	C₂²	1	32	yes	complemented
36	Q₈×D₅₂	C₂²	1	16	yes	complemented
37	#11719260	C₂²	1	48	yes	complemented
38	#11719259	C₂²	1	96	yes	complemented
39	D₄×D₅₂	C₂²	1	48	yes	complemented
40	#11719229	C₂²	1	96	yes	complemented
41	C₂×#88151	C₂²	1	6	yes	complemented
42	C₂×#88151	C₂²	1	6	yes	complemented
43	C₂×#88149	C₂²	1	6	yes	complemented
44	C₂×#88149	C₂²	1	6	yes	complemented
45	C₂×#88140	C₂²	1	12	yes	complemented
46	C₂×#88136	C₂²	1	12	yes	complemented
47	#11719182	C₂²	1	48	yes	complemented
48	C₂×#88129	C₂²	1	6	yes	complemented
49	C₂×#88128	C₂²	1	3	yes	complemented
50	C₂×C₄×D₅₂	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₅₂	C₂²	1	3	yes	—
52	C₂×C₄×D₅₂	C₂²	1	48	yes	complemented
53	C₂×C₄×D₅₂	C₂²	1	6	yes	complemented
54	C₂×C₄×D₅₂	C₂²	1	3	yes	complemented
55	C₂×C₄×D₅₂	C₂²	1	6	yes	complemented
56	C₂×C₄×D₅₂	C₂²	1	3	yes	complemented
57	C₂×C₄×D₅₂	C₂²	1	6	yes	complemented
58	C₂×#88123	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₃	C₂³	1	6	yes	—
60	C₂×C₁₃×#41	D₄	1	16	yes	complemented
61	C₂×C₁₃×#41	C₂³	1	8	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
67	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
68	C₂³×Dic₁₃	C₂³	1	6	yes	—
69	#41×D₁₃	—	2	256	no	—
70	C₂×#6131	—	2	16	no	—
71	C₂×#6131	C₂³	1	16	yes	complemented
72	C₂×Q₈×D₁₃	—	2	16	no	—
73	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
74	C₂×#6129	—	2	48	no	—
75	C₂×#6129	C₂³	1	48	yes	complemented
76	C₂×D₄×D₁₃	—	2	48	no	—
77	C₂×D₄×D₁₃	C₂³	1	48	yes	complemented
78	C₂×#6127	—	2	48	no	—
79	C₂×#6127	C₂³	1	48	yes	complemented
80	C₂²×D₅₂	—	2	24	no	—
81	C₂²×D₅₂	C₂³	1	3	yes	—
82	C₂²×D₅₂	C₂³	1	6	yes	—
83	C₂²×D₅₂	C₂³	1	24	yes	—
84	C₂²×D₅₂	C₂³	1	6	yes	—
85	C₂²×D₅₂	C₂³	1	6	yes	—
86	C₂²×D₅₂	C₂³	1	1	yes	characteristic
87	C₂²×C₄×D₁₃	—	2	48	no	—
88	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
89	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
90	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
91	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
92	C₂²×C₄×D₁₃	C₂³	1	48	yes	complemented
93	C₂²×Dic₂₆	C₂³	1	6	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
95	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
96	C₄×D₄×C₁₃	C₂³	1	24	yes	complemented
97	C₄×D₄×C₁₃	C₂³	1	24	yes	complemented
98	C₁₃×#117	C₂³	1	24	yes	complemented
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
107	#88184	C₂³	1	48	yes	complemented
108	#88184	C₂³	1	48	yes	complemented
109	C₂×#6103	C₂³	1	2	yes	—
110	C₂×#6103	C₂³	1	6	yes	—
111	C₂×#6103	C₂³	1	6	yes	—
112	C₂×#6103	C₂³	1	6	yes	—
113	C₂×#6103	C₂³	1	12	yes	—
114	C₂×#6103	C₂³	1	48	yes	complemented
115	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
116	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
117	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
119	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
120	#88151	C₂³	1	48	yes	complemented
121	#88151	C₂³	1	48	yes	complemented
122	#88149	C₂³	1	48	yes	complemented
123	#88149	C₂³	1	48	yes	complemented
124	#88140	C₂³	1	96	yes	complemented
125	#88136	C₂³	1	96	yes	complemented
126	#88129	C₂³	1	48	yes	complemented
127	#88128	C₂³	1	24	yes	complemented
128	C₄×D₅₂	C₂³	1	8	yes	—
129	C₄×D₅₂	C₂³	1	24	yes	—
130	C₄×D₅₂	C₂³	1	24	yes	complemented
131	C₄×D₅₂	C₂³	1	48	yes	complemented
132	C₄×D₅₂	C₂³	1	48	yes	complemented
133	C₄×D₅₂	C₂³	1	24	yes	complemented
134	C₄×D₅₂	C₂³	1	48	yes	complemented
135	#88123	C₂³	1	24	yes	complemented
136	C₂×D₄×#41	—	13	1	no	maximal, Sylow
137	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
138	C₂³×D₁₃	—	2	24	no	—
139	C₂³×D₁₃	—	2	24	no	—
140	C₂³×D₁₃	—	4	12	no	—
141	C₂³×D₁₃	C₂⁴	1	6	yes	—
142	C₂³×D₁₃	C₂⁴	1	24	yes	—
143	C₂³×D₁₃	C₂⁴	1	2	yes	—
144	C₁₃×#41	C₂×D₄	1	64	yes	complemented
145	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
146	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
148	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
149	C₂²×C₄×C₁₃	—	2	12	no	—
150	C₂²×C₄×C₁₃	—	4	6	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
152	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₂²⋊D₁₃	—	2	48	no	—
162	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
163	C₂²×Dic₁₃	—	2	24	no	—
164	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
165	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
166	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
167	#6131	—	2	64	no	—
168	Q₈×D₁₃	—	2	64	no	—
169	#6129	—	2	192	no	—
170	D₄×D₁₃	—	2	192	no	—
171	#6127	—	2	192	no	—
172	C₂×D₅₂	—	2	24	no	—
173	C₂×D₅₂	—	2	24	no	—
174	C₂×D₅₂	—	2	12	no	—
175	C₂×D₅₂	—	2	96	no	—
176	C₂×D₅₂	—	4	12	no	—
177	C₂×D₅₂	#41	1	8	yes	direct product factor
178	C₂×D₅₂	C₂⁴	1	12	yes	—
179	C₂×D₅₂	C₂⁴	1	24	yes	—
180	C₂×D₅₂	C₂⁴	1	24	yes	—
181	C₂×D₅₂	C₂⁴	1	24	yes	—
182	C₂×D₅₂	C₂⁴	1	4	yes	—
183	C₂×C₄×D₁₃	—	2	8	no	—
184	C₂×C₄×D₁₃	—	2	24	no	—
185	C₂×C₄×D₁₃	—	2	24	no	—
186	C₂×C₄×D₁₃	—	2	24	no	—
187	C₂×C₄×D₁₃	—	2	192	no	—
188	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
189	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
190	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
191	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
192	C₂×Dic₂₆	—	2	24	no	—
193	C₂×Dic₂₆	C₂⁴	1	24	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
196	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
197	C₄²×C₁₃	C₂⁴	1	12	yes	—
198	C₄²×C₁₃	C₂⁴	1	4	yes	—
199	C₄²×C₁₃	C₂⁴	1	12	yes	—
200	C₄²×C₁₃	C₂⁴	1	12	yes	—
201	#6103	C₂⁴	1	8	yes	—
202	#6103	C₂⁴	1	24	yes	—
203	#6103	C₂⁴	1	24	yes	—
204	#6103	C₂⁴	1	24	yes	—
205	#6103	C₂⁴	1	48	yes	—
206	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
207	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
208	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
209	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
210	C₂³×#41	—	13	2	no	—
211	D₄×#41	—	13	32	no	—
212	C₂×#550	—	13	1	no	—
213	C₂×D₄×Q₈	—	13	1	no	—
214	C₂×#548	—	13	2	no	—
215	C₂×#547	—	13	3	no	—
216	C₂×#546	—	13	6	no	—
217	C₂×D₄²	—	13	3	no	—
218	C₂×#532	—	13	3	no	—
219	C₂×#525	—	13	6	no	—
220	C₂×C₄×#41	D₁₃	1	1	yes	characteristic, complemented
221	C₂²×C₄×D₄	—	13	3	no	—
222	C₂³×C₁₃	—	2	6	no	—
223	C₂³×C₁₃	—	2	6	no	—
224	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
225	C₂³×C₁₃	C₂⁵	1	6	yes	—
226	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₂²×D₁₃	—	2	4	no	—
228	C₂²×D₁₃	—	2	4	no	—
229	C₂²×D₁₃	—	2	12	no	—
230	C₂²×D₁₃	—	2	48	no	—
231	C₂²×D₁₃	—	2	12	no	—
232	C₂²×D₁₃	—	2	12	no	—
233	C₂²×D₁₃	—	2	48	no	—
234	C₂²×D₁₃	—	4	24	no	—
235	C₂²×D₁₃	—	4	96	no	—
236	C₂²×D₁₃	C₂×#41	1	8	yes	complemented
237	C₂²×D₁₃	C₂⁵	1	12	yes	—
238	C₂²×D₁₃	C₂⁵	1	4	yes	—
239	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
240	D₄×C₁₃	C₂²×D₄	1	48	yes	complemented
241	C₂×C₄×C₁₃	—	2	6	no	—
242	C₂×C₄×C₁₃	—	2	6	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	24	no	—
245	C₂×C₄×C₁₃	—	4	12	no	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	complemented
249	C₂×C₄×C₁₃	C₂×#41	1	4	yes	complemented
250	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
256	C₂²⋊D₁₃	—	2	96	no	—
257	C₂×Dic₁₃	—	2	12	no	—
258	C₂×Dic₁₃	—	2	4	no	—
259	C₂×Dic₁₃	—	2	48	no	—
260	C₂×Dic₁₃	C₂⁵	1	12	yes	—
261	C₂×Dic₁₃	C₂⁵	1	4	yes	—
262	D₅₂	—	2	48	no	—
263	D₅₂	—	2	48	no	—
264	D₅₂	—	2	24	no	—
265	D₅₂	—	4	24	no	—
266	D₅₂	C₂×#41	1	16	yes	direct product factor
267	C₄×D₁₃	—	2	16	no	—
268	C₄×D₁₃	—	2	48	no	—
269	C₄×D₁₃	—	2	48	no	—
270	C₄×D₁₃	—	2	48	no	—
271	Dic₂₆	—	2	48	no	—
272	C₂²×#41	—	13	32	no	—
273	C₂²×#41	—	13	2	no	—
274	C₂²×#41	—	13	6	no	—
275	C₂²×#41	—	13	6	no	—
276	C₂²×#41	—	26	32	no	—
277	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
278	C₂³×Q₈	—	13	2	no	—
279	C₂³×D₄	—	13	6	no	—
280	C₂³×D₄	—	13	3	no	—
281	C₂⁴×C₄	—	13	6	no	—
282	#550	—	13	16	no	—
283	D₄×Q₈	—	13	16	no	—
284	#548	—	13	32	no	—
285	#547	—	13	48	no	—
286	#546	—	13	96	no	—
287	D₄²	—	13	48	no	—
288	#532	—	13	48	no	—
289	C₂×C₄⋊Q₈	—	13	3	no	—
290	C₂×#127	—	13	3	no	—
291	C₂×#124	—	13	6	no	—
292	#525	—	13	96	no	—
293	C₂×#123	—	13	12	no	—
294	C₂×C₂²⋊Q₈	—	13	6	no	—
295	C₂×C₂²⋊Q₈	—	13	6	no	—
296	C₂×#121	—	13	6	no	—
297	C₂×#121	—	13	6	no	—
298	C₂×#121	—	13	6	no	—
299	C₂×#121	—	13	6	no	—
300	C₂×#120	—	13	12	no	—
301	C₄×#41	C₂×D₁₃	1	16	yes	complemented
302	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
303	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
304	C₂×C₄×D₄	—	13	1	no	—
305	C₂×C₄×D₄	—	13	3	no	—
306	C₂×C₄×D₄	—	13	6	no	—
307	C₂×C₄×D₄	—	13	3	no	—
308	C₂×C₄×D₄	—	13	6	no	—
309	C₂×C₄×D₄	—	13	3	no	—
310	C₂×C₄×D₄	—	13	6	no	—
311	C₂×C₄×D₄	—	13	48	no	—
312	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	complemented
313	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	complemented
314	C₂×#117	C₂×D₁₃	1	3	yes	complemented
315	C₂²×C₄⋊C₄	—	13	3	no	—
316	C₂²×C₂²⋊C₄	—	13	6	no	—
317	C₂²×C₄²	C₂×D₁₃	1	3	yes	complemented
318	C₂²×C₁₃	—	2	6	no	—
319	C₂²×C₁₃	—	2	6	no	—
320	C₂²×C₁₃	—	2	24	no	—
321	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
322	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
323	C₂²×C₁₃	C₂²×#41	1	2	yes	—
324	C₂²×C₁₃	#585	1	2	yes	—
325	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
326	C₂×D₁₃	—	2	4	no	—
327	C₂×D₁₃	—	2	4	no	—
328	C₂×D₁₃	—	2	16	no	—
329	C₂×D₁₃	—	2	12	no	—
330	C₂×D₁₃	—	2	12	no	—
331	C₂×D₁₃	—	2	12	no	—
332	C₂×D₁₃	—	4	96	no	—
333	C₂×D₁₃	—	4	24	no	—
334	C₂×D₁₃	C₂²×#41	1	8	yes	complemented
335	C₄×C₁₃	—	2	6	no	—
336	C₄×C₁₃	—	2	6	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	C₂³×D₄	1	12	yes	—
339	C₄×C₁₃	C₂³×D₄	1	4	yes	—
340	C₄×C₁₃	C₂²×#41	1	4	yes	complemented
341	Dic₁₃	—	2	12	no	—
342	Dic₁₃	—	2	4	no	—
343	C₂⁵	—	13	6	no	—
344	C₂×#41	—	13	16	no	—
345	C₂×#41	—	13	48	no	—
346	C₂×#41	—	13	48	no	—
347	C₂×#41	—	26	256	no	—
348	C₂×#41	—	26	16	no	—
349	C₂×#41	—	26	48	no	—
350	C₂×#41	—	26	48	no	—
351	C₂×#41	D₅₂	1	16	yes	direct product factor
352	C₂×#41	C₂²×D₁₃	1	8	yes	—
353	C₂²×Q₈	—	13	16	no	—
354	C₂²×Q₈	—	13	6	no	—
355	C₂²×Q₈	—	26	16	no	—
356	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
357	C₂²×D₄	—	13	12	no	—
358	C₂²×D₄	—	13	48	no	—
359	C₂²×D₄	—	13	1	no	—
360	C₂²×D₄	—	13	6	no	—
361	C₂²×D₄	—	13	3	no	—
362	C₂²×D₄	—	13	24	no	—
363	C₂²×D₄	—	13	6	no	—
364	C₂²×D₄	—	13	6	no	—
365	C₂²×D₄	—	26	24	no	—
366	C₂²×D₄	—	26	48	no	—
367	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
368	C₂³×C₄	—	13	6	no	—
369	C₂³×C₄	—	13	6	no	—
370	C₂³×C₄	—	13	6	no	—
371	C₂³×C₄	—	13	48	no	—
372	C₂³×C₄	—	13	2	no	—
373	C₂³×C₄	—	13	6	no	—
374	C₂³×C₄	—	26	48	no	—
375	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
376	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
377	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
378	C₄⋊Q₈	—	13	24	no	—
379	#127	—	13	24	no	—
380	#124	—	13	48	no	—
381	#123	—	13	96	no	—
382	C₂²⋊Q₈	—	13	48	no	—
383	C₂²⋊Q₈	—	13	48	no	—
384	#121	—	13	48	no	—
385	#121	—	13	48	no	—
386	#121	—	13	48	no	—
387	#121	—	13	48	no	—
388	#120	—	13	96	no	—
389	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
390	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
391	C₄×D₄	—	13	8	no	—
392	C₄×D₄	—	13	48	no	—
393	C₄×D₄	—	13	24	no	—
394	C₄×D₄	—	13	24	no	—
395	C₄×D₄	—	13	48	no	—
396	C₄×D₄	—	13	24	no	—
397	C₄×D₄	—	13	48	no	—
398	C₄×D₄	C₂²×D₁₃	1	24	yes	complemented
399	C₄×D₄	C₂²×D₁₃	1	24	yes	complemented
400	#117	C₂²×D₁₃	1	24	yes	complemented
401	C₂×C₄⋊C₄	—	13	1	no	—
402	C₂×C₄⋊C₄	—	13	3	no	—
403	C₂×C₄⋊C₄	—	13	6	no	—
404	C₂×C₄⋊C₄	—	13	24	no	—
405	C₂×C₄⋊C₄	—	13	6	no	—
406	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
407	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
408	C₂×C₂²⋊C₄	—	13	2	no	—
409	C₂×C₂²⋊C₄	—	13	6	no	—
410	C₂×C₂²⋊C₄	—	13	6	no	—
411	C₂×C₂²⋊C₄	—	13	6	no	—
412	C₂×C₂²⋊C₄	—	13	48	no	—
413	C₂×C₂²⋊C₄	—	13	12	no	—
414	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
415	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
416	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
417	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
418	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
419	C₂×C₄²	C₂²×D₁₃	1	24	yes	complemented
420	C₂×C₁₃	—	2	12	no	—
421	C₂×C₁₃	D₄×#41	1	4	yes	complemented
422	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
423	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
424	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
425	D₁₃	—	2	8	no	—
426	D₁₃	—	4	12	no	—
427	C₂⁴	—	13	2	no	—
428	C₂⁴	—	13	6	no	—
429	C₂⁴	—	13	24	no	—
430	C₂⁴	—	26	24	no	—
431	C₂⁴	—	26	24	no	—
432	C₂⁴	—	52	12	no	—
433	C₂⁴	C₂³×D₁₃	1	3	yes	—
434	#41	—	26	64	no	—
435	#41	—	26	192	no	—
436	#41	—	26	192	no	—
437	#41	C₂×D₅₂	1	64	yes	direct product factor
438	C₂×Q₈	—	13	24	no	—
439	C₂×Q₈	—	26	64	no	—
440	C₂×Q₈	—	26	24	no	—
441	C₂×Q₈	C₂×D₅₂	1	8	yes	complemented
442	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
443	C₂×D₄	—	13	48	no	—
444	C₂×D₄	—	13	8	no	—
445	C₂×D₄	—	13	4	no	—
446	C₂×D₄	—	13	24	no	—
447	C₂×D₄	—	13	12	no	—
448	C₂×D₄	—	13	24	no	—
449	C₂×D₄	—	13	24	no	—
450	C₂×D₄	—	26	96	no	—
451	C₂×D₄	—	26	24	no	—
452	C₂×D₄	—	26	48	no	—
453	C₂×D₄	—	26	192	no	—
454	C₂×D₄	—	26	24	no	—
455	C₂×D₄	—	26	12	no	—
456	C₂×D₄	—	52	12	no	—
457	C₂×D₄	C₂×D₅₂	1	24	yes	complemented
458	C₂×D₄	C₂³×D₁₃	1	12	yes	—
459	C₂²×C₄	—	2	12	no	—
460	C₂²×C₄	—	4	6	no	—
461	C₂²×C₄	—	13	2	no	—
462	C₂²×C₄	—	13	6	no	—
463	C₂²×C₄	—	13	24	no	—
464	C₂²×C₄	—	13	8	no	—
465	C₂²×C₄	—	13	24	no	—
466	C₂²×C₄	—	13	24	no	—
467	C₂²×C₄	—	13	24	no	—
468	C₂²×C₄	—	26	24	no	—
469	C₂²×C₄	—	26	8	no	—
470	C₂²×C₄	—	26	24	no	—
471	C₂²×C₄	—	26	24	no	—
472	C₂²×C₄	—	26	24	no	—
473	C₂²×C₄	—	26	192	no	—
474	C₂²×C₄	C₂×D₅₂	1	24	yes	complemented
475	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
477	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
478	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
479	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
480	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
481	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
482	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
484	C₄⋊C₄	—	13	4	no	—
485	C₄⋊C₄	—	13	12	no	—
486	C₄⋊C₄	—	13	24	no	—
487	C₄⋊C₄	—	13	24	no	—
488	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
489	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
490	C₂²⋊C₄	—	13	8	no	—
491	C₂²⋊C₄	—	13	24	no	—
492	C₂²⋊C₄	—	13	24	no	—
493	C₂²⋊C₄	—	13	24	no	—
494	C₂²⋊C₄	—	13	48	no	—
495	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
496	C₄²	C₂³×D₁₃	1	4	yes	—
497	C₄²	C₂³×D₁₃	1	12	yes	—
498	C₄²	C₂³×D₁₃	1	12	yes	—
499	C₄²	C₂³×D₁₃	1	12	yes	—
500	C₁₃	C₂×D₄×#41	1	1	yes	characteristic, complemented, Sylow
501	C₂³	—	2	6	no	—
502	C₂³	—	2	6	no	—
503	C₂³	—	13	8	no	—
504	C₂³	—	13	4	no	—
505	C₂³	—	13	12	no	—
506	C₂³	—	26	48	no	—
507	C₂³	—	26	4	no	—
508	C₂³	—	26	4	no	—
509	C₂³	—	26	48	no	—
510	C₂³	—	26	12	no	—
511	C₂³	—	26	12	no	—
512	C₂³	—	26	12	no	—
513	C₂³	—	52	24	no	—
514	C₂³	—	52	96	no	—
515	C₂³	C₂²×D₅₂	1	12	yes	—
516	C₂³	C₂⁴×D₁₃	1	6	yes	—
517	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
518	Q₈	—	26	48	no	—
519	Q₈	C₂²×D₅₂	1	16	yes	complemented
520	D₄	—	13	16	no	—
521	D₄	—	26	48	no	—
522	D₄	—	26	96	no	—
523	D₄	—	26	48	no	—
524	D₄	—	26	24	no	—
525	D₄	—	52	24	no	—
526	D₄	C₂²×D₅₂	1	48	yes	complemented
527	C₂×C₄	—	2	6	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	6	no	—
530	C₂×C₄	—	2	24	no	—
531	C₂×C₄	—	4	12	no	—
532	C₂×C₄	—	13	4	no	—
533	C₂×C₄	—	13	12	no	—
534	C₂×C₄	—	26	4	no	—
535	C₂×C₄	—	26	12	no	—
536	C₂×C₄	—	26	48	no	—
537	C₂×C₄	—	26	16	no	—
538	C₂×C₄	—	26	48	no	—
539	C₂×C₄	—	26	48	no	—
540	C₂×C₄	—	26	48	no	—
541	C₂×C₄	C₂²×D₅₂	1	4	yes	—
542	C₂×C₄	C₂²×D₅₂	1	12	yes	—
543	C₂×C₄	C₂²×D₅₂	1	48	yes	complemented
544	C₂×C₄	#41×D₁₃	1	4	yes	complemented
545	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
546	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
547	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
548	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
549	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
550	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
551	C₂²	—	2	24	no	—
552	C₂²	—	2	6	no	—
553	C₂²	—	2	6	no	—
554	C₂²	—	13	8	no	—
555	C₂²	—	26	16	no	—
556	C₂²	—	26	4	no	—
557	C₂²	—	26	4	no	—
558	C₂²	—	26	12	no	—
559	C₂²	—	26	12	no	—
560	C₂²	—	26	12	no	—
561	C₂²	—	52	96	no	—
562	C₂²	—	52	24	no	—
563	C₂²	C₂³×D₅₂	1	12	yes	—
564	C₂²	C₂³×D₅₂	1	2	yes	—
565	C₂²	C₂×#41×D₁₃	1	2	yes	—
566	C₂²	#11719648	1	2	yes	—
567	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
568	C₄	—	2	6	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	6	no	—
571	C₄	—	26	4	no	—
572	C₄	—	26	12	no	—
573	C₄	C₂³×D₅₂	1	4	yes	—
574	C₄	C₂³×D₅₂	1	12	yes	—
575	C₄	C₂×#41×D₁₃	1	4	yes	complemented
576	C₂	—	2	12	no	—
577	C₂	—	26	8	no	—
578	C₂	—	52	12	no	—
579	C₂	#41×D₅₂	1	4	yes	direct product factor
580	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
581	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
582	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	C₂×D₄×#41
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×#41×D₁₃	C₂	semidirect
2. #41×D₅₂	C₂	direct (N × H)
3. C₂×#11719282	C₂	semidirect
4. C₂×Q₈×D₅₂	C₂	semidirect
5. C₂×#11719281	C₂	semidirect
6. C₂×#11719260	C₂	semidirect
7. C₂×#11719259	C₂	semidirect
8. C₂×D₄×D₅₂	C₂	semidirect
9. C₂×#11719182	C₂	semidirect
10. C₂×#11719229	C₂	semidirect
11. C₂²×C₄×D₅₂	C₂	semidirect
12. C₂×C₄×C₁₃×#41	C₂	semidirect
15. C₂×#41×D₁₃	C₂²	semidirect
16. C₂²×#6131	C₂²	semidirect
17. C₂²×Q₈×D₁₃	C₂²	semidirect
18. C₂²×#6129	C₂²	semidirect
19. C₂²×D₄×D₁₃	C₂²	semidirect
20. C₂²×#6127	C₂²	semidirect
22. C₂³×C₄×D₁₃	C₂²	semidirect
23. C₄×C₁₃×#41	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. C₂×C₁₃×#117	C₂²	semidirect
29. C₂²×C₄²×C₁₃	C₂²	semidirect
30. C₂×#88184	C₂²	semidirect
31. C₂×#88184	C₂²	semidirect
32. C₂²×#6103	C₂²	semidirect
33. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
34. #11719282	C₂²	semidirect
35. #11719281	C₂²	semidirect
36. Q₈×D₅₂	C₂²	semidirect
37. #11719260	C₂²	semidirect
38. #11719259	C₂²	semidirect
39. D₄×D₅₂	C₂²	semidirect
40. #11719229	C₂²	semidirect
41. C₂×#88151	C₂²	semidirect
42. C₂×#88151	C₂²	semidirect
43. C₂×#88149	C₂²	semidirect
44. C₂×#88149	C₂²	semidirect
45. C₂×#88140	C₂²	semidirect
46. C₂×#88136	C₂²	semidirect
47. #11719182	C₂²	semidirect
48. C₂×#88129	C₂²	semidirect
49. C₂×#88128	C₂²	semidirect
52. C₂×C₄×D₅₂	C₂²	semidirect
53. C₂×C₄×D₅₂	C₂²	semidirect
54. C₂×C₄×D₅₂	C₂²	semidirect
55. C₂×C₄×D₅₂	C₂²	semidirect
56. C₂×C₄×D₅₂	C₂²	semidirect
57. C₂×C₄×D₅₂	C₂²	semidirect
58. C₂×#88123	C₂²	semidirect
60. C₂×C₁₃×#41	D₄	semidirect
71. C₂×#6131	C₂³	semidirect
73. C₂×Q₈×D₁₃	C₂³	semidirect
75. C₂×#6129	C₂³	semidirect
77. C₂×D₄×D₁₃	C₂³	semidirect
79. C₂×#6127	C₂³	semidirect
92. C₂²×C₄×D₁₃	C₂³	semidirect
94. C₄×Q₈×C₁₃	C₂³	semidirect
95. C₄×Q₈×C₁₃	C₂³	semidirect
96. C₄×D₄×C₁₃	C₂³	semidirect
97. C₄×D₄×C₁₃	C₂³	semidirect
98. C₁₃×#117	C₂³	semidirect
106. C₂×C₄²×C₁₃	C₂³	semidirect
107. #88184	C₂³	semidirect
108. #88184	C₂³	semidirect
114. C₂×#6103	C₂³	semidirect
119. C₂×C₄⋊Dic₁₃	C₂³	semidirect
120. #88151	C₂³	semidirect
121. #88151	C₂³	semidirect
122. #88149	C₂³	semidirect
123. #88149	C₂³	semidirect
124. #88140	C₂³	semidirect
125. #88136	C₂³	semidirect
126. #88129	C₂³	semidirect
127. #88128	C₂³	semidirect
130. C₄×D₅₂	C₂³	semidirect
131. C₄×D₅₂	C₂³	semidirect
132. C₄×D₅₂	C₂³	semidirect
133. C₄×D₅₂	C₂³	semidirect
134. C₄×D₅₂	C₂³	semidirect
135. #88123	C₂³	semidirect
144. C₁₃×#41	C₂×D₄	semidirect
145. C₂×Q₈×C₁₃	C₂×D₄	semidirect
147. C₂×D₄×C₁₃	C₂×D₄	semidirect
151. C₂²×C₄×C₁₃	C₂×D₄	semidirect
177. C₂×D₅₂	#41	direct (N × H)
220. C₂×C₄×#41	D₁₃	semidirect
236. C₂²×D₁₃	C₂×#41	semidirect
239. Q₈×C₁₃	C₂²×D₄	semidirect
240. D₄×C₁₃	C₂²×D₄	semidirect
248. C₂×C₄×C₁₃	C₂²×D₄	semidirect
249. C₂×C₄×C₁₃	C₂×#41	semidirect
266. D₅₂	C₂×#41	direct (N × H)
301. C₄×#41	C₂×D₁₃	semidirect
302. C₂×C₄×Q₈	C₂×D₁₃	semidirect
303. C₂×C₄×Q₈	C₂×D₁₃	semidirect
312. C₂×C₄×D₄	C₂×D₁₃	semidirect
313. C₂×C₄×D₄	C₂×D₁₃	semidirect
314. C₂×#117	C₂×D₁₃	semidirect
317. C₂²×C₄²	C₂×D₁₃	semidirect
334. C₂×D₁₃	C₂²×#41	semidirect
340. C₄×C₁₃	C₂²×#41	semidirect
351. C₂×#41	D₅₂	direct (N × H)
389. C₄×Q₈	C₂²×D₁₃	semidirect
390. C₄×Q₈	C₂²×D₁₃	semidirect
398. C₄×D₄	C₂²×D₁₃	semidirect
399. C₄×D₄	C₂²×D₁₃	semidirect
400. #117	C₂²×D₁₃	semidirect
419. C₂×C₄²	C₂²×D₁₃	semidirect
421. C₂×C₁₃	D₄×#41	semidirect
437. #41	C₂×D₅₂	direct (N × H)
441. C₂×Q₈	C₂×D₅₂	semidirect
457. C₂×D₄	C₂×D₅₂	semidirect
474. C₂²×C₄	C₂×D₅₂	semidirect
500. C₁₃	C₂×D₄×#41	semidirect
519. Q₈	C₂²×D₅₂	semidirect
526. D₄	C₂²×D₅₂	semidirect
543. C₂×C₄	C₂²×D₅₂	semidirect
544. C₂×C₄	#41×D₁₃	semidirect
575. C₄	C₂×#41×D₁₃	semidirect
579. C₂	#41×D₅₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#41×D₁₃	2
#41×D₅₂	2
C₂×#11719282	2
C₂×Q₈×D₅₂	2
C₂×#11719281	2
C₂×#11719260	2
C₂×#11719259	2
C₂×D₄×D₅₂	2
C₂×#11719182	2
C₂×#11719229	2
C₂²×C₄×D₅₂	2
C₂×C₄×C₁₃×#41	2
C₂×D₄×#41	13

Subgroups — C2×#41×D52 #16769882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×D₅₂ #16769882